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Conceived and designed the experiments: SIV MM MBM NJS WGI. Performed the experiments: SIV MM MBM. Analyzed the data: SIV MM MBM. Contributed reagents/materials/analysis tools: SIV MM MBM LNL WGI. Wrote the paper: SIV MM MBM NJS WGI.

The authors have declared that no competing interests exist.

In a sample of 3,187 twins and 3,294 of their parents, we sought to investigate association of both individual variants and a genotype-based height score involving 176 of the 180 common genetic variants with adult height identified recently by the GIANT consortium. First, longitudinal observations on height spanning pre-adolescence through adulthood in the twin sample allowed us to investigate the separate effects of the previously identified SNPs on pre-pubertal height and pubertal growth spurt. We show that the effect of SNPs identified by the GIANT consortium is primarily on prepubertal height. Only one SNP, rs7759938 in

We evaluated the developmental specificity of 176 SNPs known to affect adult height based on meta-analysis from the GIANT consortium. First, longitudinal observations on height spanning pre-adolescence through adulthood in a twin sample allowed us to investigate the individual effects of the previously identified SNPs on both pre-pubertal height and pubertal growth spurt. We show that the effect of the SNPs identified by the GIANT consortium is primarily on prepubertal height. Only one SNP, rs7759938 in

Adult height is a model multigenic phenotype for genetic association studies. Twin and adoption studies suggest that height is highly heritable (∼80%)

For any person adult height reflects roughly two decades of growth. Change in height is relatively rapid throughout infancy, slows down in early childhood, and increases again during puberty when a notable growth spurt occurs

The sample (N = 6481) was drawn from Caucasian participants in the Minnesota Twin Family Study (MTFS). The MTFS a 20-year, longitudinal, community-representative study conducted at the University of Minnesota and approved by the University of Minnesota Institutional Review Board continuously since inception. The study has been extensively described previously

Males | Females | |||||||||

N | MZ Pairs | DZ Pairs | Age (Mean SD) | Height in cm (Mean SD) | N | MZ Pairs | DZ Pairs | Age (Mean SD) | Height in cm (Mean SD) | |

Age 11 | 1016 | 327 | 168 | 11.78 (.40) | 150.09 (7.80) | 1012 | 315 | 179 | 11.76 (.45) | 151.64 (7.68) |

Age 14 | 880 | 281 | 146 | 14.85 (.48) | 170.90 (8.19) | 892 | 273 | 159 | 14.82 (.54) | 163.79 (6.22) |

Age 17 | 1170 | 371 | 196 | 17.71 (.51) | 177.78 (6.74) | 1320 | 425 | 218 | 17.75 (.59) | 164.97 (6.32) |

Age 20 | 916 | 287 | 142 | 21.31 (.86) | 178.88 (6.65) | 1126 | 348 | 195 | 20.76 (.56) | 165.50 (6.35) |

Age 24 | 817 | 242 | 130 | 24.72 (.96) | 178.95 (6.61) | 509 | 154 | 90 | 25.05 (.60) | 166.42 (6.46) |

Age 29 | 728 | 210 | 116 | 29.45 (.54) | 179.17 (6.58) | 566 | 178 | 85 | 29.49 (.51) | 165.51 (6.17) |

The twin sample was used to develop a genetically mediated, longitudinal growth model for height. There are many approaches to analysis of longitudinal designs, and choosing the best approach often requires assumptions about, or explicit knowledge of, the (unknown) true growth trajectories generating the data

The growth model was constructed on the twins to evaluate SNP effects on age-11 height and pubertal growth after age 11. In the growth model, age-11 height corresponds to the intercept and pubertal growth corresponds to the slope. A diagram of the model is depicted in

Measurements of height were taken at approximately ages 11, 14, 17, 20, 24, and 29. The measurements are adjusted for covariates, and then modeled as a function of a random intercept, representing age-11 height, and a random slope, representing growth in height from age 11 to adulthood, and a residual, which for convenience of presentation is not depicted in the figure. The intercept and the slope are allowed to correlate (this is represented as the double-headed arrow connecting them). The loadings of the slope onto height (denoted _{11}–_{29}) are the ages of participants during each of the assessments. The slope is piecewise linear in age, with the maximum age constrained to be 18 in males and 16 in males (see text for details). The effect of a SNP on the intercept and slope (denoted _{i} and _{s}, respectively) can be estimated directly. The growth model extension to twins is portrayed in the inset box. By taking advantage of twin zygosity, the variance in the intercept and slope are partitioned into additive genetic (A), shared environmental (C), and unshared environmental (E) components. The correlation between the intercept and slope can also be decomposed in this way (e.g., _{g} would be the genetic correlation, _{c}_{ig} and _{sg}, respectively.

In the path diagram of the phenotypic model (

An important caveat with the proposed growth model as described in

As portrayed in

Analogous to the phenotypic growth model is the twin growth model, partially displayed in the box inset in

With the proposed growth model, we could estimate the effect of SNPs on the intercept (i.e., height at age 10.75, the earliest age at which any participant was assessed) and slope (i.e., pubertal growth). Using twins, we could further estimate the influence of SNP effects on genetic variance—as opposed to overall phenotypic variance—thus providing a direct estimate of the genetic variance accounted for by the SNPs. Studies on height heretofore have been unable to accomplish this, and have been restricted to comparing estimates of the percent of variance accounted for by SNPs in their sample to estimates of heritability obtained in separate studies of twins (e.g., as in refs

There is considerable variation in age of pubertal onset. To obtain a more accurate measure of pubertal age (versus chronological age) we used the Pubertal Development Scale

Age of Assessment | Mean | Median | SD | Correlation with age at that assessment | Correlation with height at that assessment |

Males | |||||

Age-11 Puberty | 1.3 | 1.3 | 0.49 | 0.21 | 0.28 |

Age-14 Puberty | 2.7 | 2.8 | 0.58 | 0.35 | 0.47 |

Females | |||||

Age-11 Puberty | 2.2 | 2.3 | 0.64 | 0.28 | 0.51 |

Age-14 Puberty | 3.3 | 3.3 | 0.44 | 0.28 | 0.21 |

We incorporated pubertal status into the growth model in the following way. For each age of assessment we regressed height on age and puberty score and, for females, an indicator variable measuring whether menarche had occurred by that assessment. For males both age and puberty score were highly significant in predicting height at age 11 (r^{2} = .17, p<2e^{−16}) and 14 (r^{2} = .23, p<2e^{−16}). In females at age 11 age, puberty score, and menarche significantly predicted height (r^{2} = .32, p<2e^{−16}). At age 14 only the puberty score was a significant predictor (r^{2} = .04, p = 8.4e^{−9}). We computed the sum of age and puberty score (and menarche for females) weighted by their corresponding regression weight and scaled the result to have the mean and variance of the original chronological age at 11 and 14. This gives an estimate of each subject's pubertal age—as opposed to chronological age—as it relates to growth in height. In supplementary analyses these pubertal ages were used in place of chronological age for the age-11 and age-14 assessments in the growth model, in an attempt to more precisely gauge the developmental specificity of each SNP.

All statistical analysis was conducted in the R Environment

SNPs were genotyped on an Illumina 660quad array using DNA derived from whole blood for approximately 90% of the sample and from saliva samples for the remainder. For quality control purposes, each 96-well plate included DNA from two members of a single CEPH family (rotated across plates) and one duplicate sample. Markers were excluded if (see ref

Of the 180 SNPs described by the GIANT consortium as associated with height, 52 existed on the Illumina 660quad. The remaining were imputed with best-guess genotypes using MaCH ^{2} = .08, .46, and .20). One SNP (rs5017948) was not contained in the 1000 Genomes 2010-06 or 2010-08 reference datasets and so was discarded. The average r^{2} of the remaining 124 imputed SNPs was .96 (SD = .07, range = [.55, 1.0]). In total, 176 of the 180 SNPs from the GIANT Consortium meta-analysis

First, we ran association tests for each of the 176 SNPs on adult height in the full sample. A subset of twins (N = 775) had not yet reached adult height and were excluded from this analysis (i.e., were male and under 18 at the time of their last assessment, or were female and under 16). To account statistically for within-family clustering a generalized least squares method was used ^{−102}) and accounted for 9.2% (95% confidence interval = [8.2%, 11.1%]) of the phenotypic variance in adult height (in the full sample N = 5706). This result is not significantly different from the r^{2} of 10.5% found by the GIANT Consortium in

On the left panel are the univariate associations for each of the 176 SNPs (of the 180 SNPs from the Allen et al.

Fitting the growth model, we found the intercept was 86% heritable (95% c.i. = [69%, 100%]) and the slope 84% heritable (65%, 100%). Shared environmental effects accounted for 9% (0%, 27%) and 11% (0%, 31%) of the variance in the intercept and slope, respectively. Unshared environment accounted for 5% (4%, 6%) in the intercept and 5% (4%, 7%) in the slope. Clearly, both age-11 height and pubertal growth (here, the intercept and slope) were highly heritable, consistent with previous reports

Individual SNP and genetic score effects on the intercept and slope were computed simultaneously. Log-transformed p-values are displayed in ^{−9}), but was chance-level for the slope (^{−13}). Alternatively, the QQ plot for pubertal growth consistently showed chance-level effects. The genetic score effect here was nominally significant (t = 2.42, df = 1652,

Univariate plot (a) and QQ plot (b) of SNP effects on intercept. Univariate plot (c) and QQ plot (d) of SNP effects on the slope. All symbols are described in the caption for

All regression coefficients, standard errors, and

To summarize findings from the growth model, we computed the variance in height accounted for by the genetic risk score's effect on the intercept and slope. A linear growth model is linear in the mean function but quadratic in the variance. In the present model, phenotypic height (

This parabola was computed for the base model, with no genetic score effect, and used to compute r^{2} with the genetic score. We plotted phenotypic r^{2} in ^{2}). The model with a genetic score effect only on the slope did account for variance in height at all ages, but not as much as the model with a score effect only on the intercept. More to the point, the model with score effect simultaneously on the slope and intercept negligibly improved over the model with score effect only on the intercept. This indicated that the score has only a slight relationship with the unique SNP variance in pubertal growth. However, because the score reduces variance in height even when it was only allowed to load onto the slope, it did appear that the score is related to genetic variance overlapping between the intercept and slope (recall the intercept and slope are genetically correlated at −.56, and we expected some genetic variants to affect both).

Green indicates the r^{2} of the score effect on phenotypic variance in height (using the growth model represented in ^{2} of the score effect on genetic variance in height (using the growth model extension to twins displayed in the inset box of ^{2}. Irrespective of phenotypic or genetic variance, allowing the score to affect only the growth model slope resulted in the lowest r^{2} for both conditions. Allowing the score to affect only the growth model intercept resulted in considerable gain in r^{2}. Most interestingly, allowing the score to simultaneously influence the slope and intercept resulted in negligible gain over allowing the score to influence the intercept only (i.e., the effect of score onto slope fixed at zero). This indicates that the score is only negligibly related to genetic variation specific to pubertal growth (slope), but rather is relevant to genetic variation that affects growth occurring up to age 11 (intercept). In addition, it provides evidence that some genetic variation indexed by the score is relevant for growth both before age 11 and from age 11 to adulthood.

Using the twins, we also computed the genetic r^{2}, or the genetic variance in height accounted for by the genetic score. This is plotted in red in ^{2} was greater than the phenotypic r^{2} for the entire age range under investigation. Comparing the maximum phenotypic r^{2} to the maximum genetic r^{2} for the model with a score effect on both the intercept and slope, one notices a jump from 9.2% (95% c.i. = [3.0%, 15.1%]) to 14.3% (95% c.i. = [0.3%, 26%]; each measured at the respective function's apex). That is, by using the twins to partition environmental variance, we were able to increase the magnitude of the SNP effect and consequently the sensitivity of the analysis.

Growth models were also fit separately to the male and female subsamples. After scaling male heights for each age of assessment to have the female's mean and variance, the growth model variance component parameters were different between the sexes (χ^{2} = 78.04, ^{−13}). While heritability of the intercept was similar (.84 for males versus .82 for females) the heritability of the slope was different (.93 versus .64, respectively). Females had a larger shared environmental contribution to their slope variance (.01 for males and .31 for females). Males and females had similar phenotypic correlations between the intercept and slope (−.66 for males and −.64 for females). The genetic and environmental contributions to this correlation were different between the sexes. The genetic correlation between intercept and slope was −.60 for males and −.47 for females. The shared environment correlation was −.04 for males and −.14 for females. The unshared environmental correlation was −.02 in males and −.03 in females.

The overall SNP association trends were similar in both sexes (i.e. larger effects on the intercept and smaller effects on the slope). All SNP and score statistics are included in

Growth model parameters did not change dramatically after correcting chronological ages at 11 and 14 for pubertal status. The negative correlation between the intercept and slope was unchanged (−.62) with a larger genetic contribution (−.58) and smaller contributions by shared environment (−.02) and unshared environment (−.03). The intercept was 88% heritable with contributions of 7% and 5% from shared and unshared environment, respectively. The slope was 84% heritable with contributions of 10% and 6% from shared and unshared environment, respectively.

SNP associations also remained largely unchanged after correcting for pubertal status.

The first wave of GWAS research has been successful in identifying numerous common variants associated with various adult disorders and traits

The present study extended genetic analysis of developmental phenotypes by implementing a growth model to partition observed measures into two biologically meaningful constructs: pre-pubertal height and pubertal growth. We focused here on an established literature of SNP effects on height. This is necessary because individual genetic effects are too small to be detected at genome-wide levels by most individual studies, and combining longitudinal studies with commensurate phenotypes can be prohibitively difficult (longitudinal data is expensive and rare, investigators gathering different data on individuals from different populations at different ages and developmental levels). It may be that consortia of cross-sectional data will largely be necessary to discover replicable genetic variants while smaller, methodologically-unique individual studies will be left to understand those effects within a developmental context.

The vast majority of SNPs identified by Allen et al.

While most SNPs were unrelated to pubertal growth, one was. rs7759938 in

We also evaluated the effect of a genetic score on zygosity-derived genetic variance, as opposed to phenotypic variance, using a sample of twins. The score accounted for 14.3% of genetic variance in adult height, but only 9.2% of phenotypic variance, illustrating the possible advantages of using a twin sample. The use of twins provides concrete advantages over analyses that estimate the fraction of heritable variance attributable to multiple loci indirectly either based on previously reported heritability estimates or genome-wide markers in unrelated individuals. Admittedly, the advantage may not be extremely powerful in the present context, given height's high heritability, where the genetic variance is 80% or more of the total phenotypic variance. However, for less-heritable phenotypes, or where heritability is less well known, the approach will provide improved information about the magnitude of a SNP's (or gene's, or pathway's) relationship to the phenotype. A growth model is not necessary to evaluate genetic r^{2}, but so-called “genetically informative” samples such as twins or adoptive families are. An array of statistical techniques have been developed for such samples

In summary, genomic findings from consortia may be fruitfully characterized within a developmental framework. Many analytic approaches exist, and the best may depend on the data structure at hand. Genetically informative samples such as twins remain important and viable tools in investigating genomic variation, even as genotyping or sequencing becomes routine.

Scatterplot Matrix of Regression Coefficients. “Meta-Analysis” refers to the SNPs reported in Allen et al.

(TIF)

(a) Refers to males; (b) to females. All other aspects are described in the caption to

(TIF)

SNP and Score Effects on the Puberty-Corrected Growth Model Intercept and Slope. Univariate plot (a) and QQ plot (b) of SNP effects on intercept. Univariate plot (c) and QQ plot (d) of SNP effects on the slope. All symbols are described in the caption for

(TIF)

Gene/allele information, regression coefficients, standard errors, and p-values for all tests in the growth model and the adult height analysis.

(XLS)

Regression Correlation Coefficient Matrix. These are Spearman rank order correlations between all 176 regression coefficients computed for each height phenotype under study. Confidence intervals were computed by bootstrap with 2000 pseudo-replications. “Meta-Analysis” refers to sex-combined regression coefficients from the GIANT Consortium meta-analysis

(DOC)